For the past two years I have, in my copious free time, been studying Richard Swinburne’s case for God. Recently my focus has been on his evaluation of the cosmological argument (hereafter TCA) in his book *The Existence of God, *2nd edition (hereafter EOG). His version of TCA is quite simple:**e: A complex physical universe exists.****Therefore****g: God exists.**

But Swinburne’s argument about TCA is not so simple.

Swinburne does not present TCA as a proof of the existence of God, nor does he claim that TCA makes God’s existence probable. Rather, he claims that *e* makes *g* more probable that it would be otherwise:**P( g**l

**l**

*e*&*k*) > P(*g*

*k*)Where

*k*is tautological (

*a priori*) background knowledge. In other words,

*e*provides relevant evidence in support of of the hypothesis

*g*, increasing the probability that

*g*is the case.

I understand most of Swinburne’s argument in support of his claim about TCA, but there is a part of his reasoning that I just don’t get, and I’m hoping that someone can help me to get it.

There are two key premises in Swinburne’s argument about TCA:

**(TCA8) The probability that there will be a complex physical universe given that God exists is at least ½. (EOG, p.151)**

**(TCA9) The probability that there will be a complex physical universe given that God does not exist is low. (EOG, p.151)**

I fully understand Swinburne’s argument for (TCA8), and I think I understand his core argument for (TCA9), but I’m having difficulty figuring out his reasoning in support of a premise used to support (TCA9). Here is how I would translate (TCA9) into a conditional probability statement:**.2 ≤ P( e**l

**~**

*g*&*k*) < .4(I’m interpreting ‘low probability’ as meaning ‘greater than or equal to .2, and less than .4’).Here is what I believe to be the core argument for (TCA9):**(TCA14) The probability that a complex physical universe exists without an explanation is very low. (EOG, p.152)****(TCA15) The probability that a complex physical universe exists given that God does not exist is approximately equal to the probability that a complex physical universe exists without an explanation. (EOG, p.149)****Therefore:(TCA13) The probability that a complex physical universe exists given that God does not exist is approximately a very low probability.**

**Therefore:**

(TCA9) The probability that there will be a complex physical universe given that God does not exist is low (at most). (EOG, p.151)

(TCA9) The probability that there will be a complex physical universe given that God does not exist is low (at most). (EOG, p.151)

I think I understand Swinburne’s reasoning in support of (TCA14), but I cannot figure out his reasoning in support of (TCA15), even after reading and re-reading what he says in support of this claim.

I’m also uncertain about how to represent (TCA14) in terms of a conditional probability statement. Here is my attempt to do so:

**0 < P(**l

*e***~**

*y*&*k*) < .2**y: e has an explanation.**

If I knew how to correctly represent (TCA14) in a conditional probability statement, perhaps that would help me to understand Swinburne’s thinking.

Swinburne eliminates the possibility that science might explain

*e,*which leaves him with just two possibilities: either e has a personal explanation (

*e*being the result of a choice of some person for some purpose) or else e has no explanation at all, and is just a brute fact.

Traditionally, cosmological arguments eliminate the possibility that the universe is simply a brute fact by an appeal to the Principle of Sufficient Reason (hereafter: PSR). But Swinburne rejects the strong version of PSR, and sees no good reason for accepting a weaker version of PSR. So, what he does is argue that the a priori probability of e being the case but having no explanation is very low, (TCA14).